Vector control method for controlling a rotor speed of an induction motor

ABSTRACT

A vector control method is provided for controlling a rotor speed of an induction motor by an inverter which provides an AC current of varying frequency to the induction motor, and a vector controller which provides control voltage Vu, Vv, Vw, in response to an excitation current command i 1d* . The excitation current command is indicative of an excitation current being fed to the induction motor, a desired rotation speed command ω r* , and a primary frequency ω, for controlling the inverter to vary the rotor speed. The method includes the steps of detecting a primary current being fed to the induction motor, analyzing the detected primary current to obtain an excitation current i 1d  and a detected torque current i 1q , multiplying a torque value represented by the detected torque current i 1q  by a predetermined motor constant K m  to obtain a slip frequency ω s , and adding the obtained slip frequency ω s  to the rotation speed command ω r*  to determine the primary frequency ω (ω=ω r*  +ω s ), calculating a deviation between the delay torque current i 1q , and the detected torque current i 1q  and supplying the deviation to a proportional plus integral controller, the proportional plus integral controller producing as an output an updated delayed torque current i 1q , as the torque value for determining the primary frequency ω.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention is directed to a vector control method forcontrolling a rotor speed of an induction motor, and more particularlyto such a vector control method for the induction motor without relyingupon a speed detector.

2. Description of the Prior Art

A vector control system for the induction motor is known in the art tobe advantageous for quick and precise control of the induction motor, inwhich a control is made to vary a frequency of a primary currentsupplied to the induction motor. U.S. Pat. No. 4,680,526 discloses avector control system for the induction motor in which the primarycurrent is analyzed to detect an excitation current and a torquecurrent. These detected currents are processed to give an estimatedrotation speed of the motor without using a speed detector. Thusestimated rotation speed is processed in relation to a speed commandsignal representative of an intended rotation speed in order to obtain arequired torque current at which the estimated rotation speed becomesequal to the intended rotation speed, after which the required torquecurrent is compared with the detected torque current for determining theprimary frequency. Thus, this method requires speed operation forobtaining the estimated rotation speed, in addition to current operationof determining the primary frequency, therefore necessitates complicatedoperations.

To avoid the complicated operations for determination of the primaryfrequency, it is contemplated to obtain a slip frequency as a product ofthe detected torque current and a predetermined motor constant, and todetermine the primary frequency as the sum of the slip frequency and athe rotation speed command signal selected by the user. However, thisscheme poses another problem that the slip frequency is directlyinfluenced by a transient variation in the torque current caused whenchanging the motor speed, i.e., changing the rotation speed commandsignal, resulting in an over-responsive variation in the primaryfrequency. Therefore, the above scheme fails to give precise speedcontrol of the motor.

SUMMARY OF THE INVENTION

The above problem has been eliminated in a vector control method for aninduction motor in accordance with the present invention which iscapable of assuring precise and consistent speed control, yet withoutrelying upon a speed detector. The vector control method of the presentinvention utilizes an inverter which provides an AC current of varyingand frequency to the induction motor, and a vector controller. Thevector controller provides control voltage Vu, Vv, Vw, in response to anexcitation current command i_(1d) * indicative of an excitation currentbeing fed to said induction motor, a desired rotation speed commandω_(r) *, and a primary frequency ω, for controlling the inverter to varya motor speed. The method comprises the steps of:

monitoring a primary current being fed to the induction motor to derivetherefrom an excitation current i_(1d) and a torque current i_(1q) ;

multiplying a torque value represented by thus detected torque currenti_(1q) by a predetermined motor constant Km to obtain a slip frequency;and

adding thus obtained slip frequency ω_(s) to the rotation speed commandω_(r) * to determine the primary frequency ω(ω=ω_(r) *+ω_(s)).

The method is characterized to delay by integration the detected torquecurrent i_(1q) in order to give a delayed torque current i_(1q) ' as thetorque value to be processed in determining the primary frequency ω. Thedelayed torque current i_(1q) ' is obtained by proportioning andintegrating a deviation between the delayed torque current i_(1q) ' andthe detected torque current i_(1q). By using thus delayed torque currentfor determination of the slip frequency ω_(s), it is possible to cancelundesired transient variation from appearing in the calculated slipfrequency and therefore the primary frequency, thereby assuring aconsistent and precise speed control, which is therefore a primaryobject of the present invention.

Additionally, the present invention provides effective methods forcorrectly determining the motor constant so as to enable more precisespeed control irrespective of possible variation in the motor constant.The motor constant is a function of a required excitation currentspecific to the motor, a primary resistance, secondary resistance and aninductance of the motor which may vary for individual motors or indifferent temperature environments.

The excitation current is acknowledged in the vector controller in theform of the excitation current command i_(1d) * which is corrected byzeroing the difference between the excitation current command i_(1d) *and the detected excitation current i_(1d) from the primary current, sothat the vector controller operates based upon thus corrected excitationcurrent command i_(1d) * to give the control voltage.

The primary resistance is input to the vector controller as a primaryresistance set value r₁ * which is corrected by zeroing a differencebetween the excitation current command i_(1d) * and the detectedexcitation current i_(1d), under a condition of supplying the primarycurrent to the induction motor while stalling the motor. The secondaryresistance is input to the vector controller as a secondary resistanceset value r₂ * which is corrected by zeroing a difference between theexcitation current command i_(1d) * and the detected excitation currenti_(1d), so that the vector controller operates based upon thus correctedsecondary resistance set value r₂ * to give the control voltage.

A primary inductance L₁ can be corrected in terms of the excitationcurrent command i_(1d) * due to the fact that flux parameter φ isconstant for the motor and is expressed as φ=L₁ ·I_(1d) *. In view ofthat the excitation current will vary due to only an error in theprimary inductance L₁ when the rotation speed is just varying, thecorrection of the excitation current in this condition can stand for thecorrection of the primary inductance. To this end, the correction of theprimary inductance L₁ is made by zeroing the difference between theexcitation current command i_(1d) * and the detected excitation currenti_(1d), under a condition of varying the rotation speed.

These and still other advantageous features will become more apparentfrom the following description of the preferred embodiments when takenin conjunction with the attached drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of a vector control system utilized inaccordance with a first embodiment of the present invention;

FIGS. 2A, 2B, 3, 4, 5 are graphs illustrating the operations of thepresent invention, respectively;

FIG. 6 is a block diagram of a vector control system in accordance witha second embodiment of the present invention;

FIG. 7 is a block diagram of a vector control system in accordance witha third embodiment of the present invention;

FIG. 8 is a block diagram of a vector control system in accordance witha fourth embodiment of the present invention;

FIGS. 9A and 9B are graphs illustrating operations of the system of FIG.8, respectively;

FIGS. 10 and 11 are block diagrams of a vector control system inaccordance with a fifth embodiment of the present invention;

FIG. 12 is a graph illustrating the operation of the system of FIGS. 10and 11;

FIG. 13 is a block diagram schematically illustrating the operation fordetermination of a motor constant Km; and

FIGS. 14 to 16 are block diagrams schematically illustrating otheroperations for determination of the motor constant Km in accordance withmodifications of the sixth embodiment.

DETAILED DESCRIPTION OF THE EMBODIMENTS

First embodiment <FIGS. 1 to 5>

Referring now to FIG. 1, there is shown a vector control systemrealizing a method in accordance with a first embodiment of the presentinvention. A three-phase induction motor 1 is driven by a voltageinverter 2 under control of a vector controller 10. The voltage inverter2 regulates an input DC voltage by a pulse width modulation (PWM) tosupply a primary AC current of varying voltage and frequency to a statorof the motor 1 for control of a rotor speed, in response to controlvoltage signals Vv, Vu, Vw generated from the vector controller 10. Acurrent sensor 4 is provided to sense the primary current being fed tothe motor to give a set of three current signals Iu, Iv, Iw which arereceived as feedback signals at the vector controller 10.

Prior to discussing the present invention, a reference is made to anoperating condition of the induction motor which are expressed by thefollowing matrix of equations in a reference (direct-quadrature) framerotating at a speed of rotor flux vector (primary frequency): ##EQU1##where V_(1d) =d-axis component of a primary (stator) voltage;

V_(1q) =q-axis component of the primary voltage;

r₁ =primary (stator) resistance;

r₂ =secondary (rotor) resistance,

L₁ =primary (stator) inductance;

L₂ =secondary (rotor) inductance;

M=mutual (stator/rotor)inductance;

σ=leakage coefficient expressed by ##EQU2## i_(1d) =excitation current,i.e., d-axis component of the primary (stator) current;

i_(1q) =torque current, i.e., q-axis component of the primary current;

ω_(s) =slip frequency;

φ_(2d) =d-axis component of secondary flux vector;

φ_(2q) =q-axis component of secondary flux vector; and

p=differential operator (=d/dt).

Additionally, the following parameters are utilized in the descriptionof the present invention:

i_(1d) *: excitation current command;

i_(1q) ': torque current signal;

ω_(r) *: rotation speed command;

ω: primary frequency;

θ: phase angle demand:

r₁ *: primary resistance set value; and

r₂ *: secondary resistance set value.

The secondary flux vectors φ_(2d) and φ_(2q) in the above matrix (1) canbe expressed respectively by the equations:

    φ.sub.2d =M·i.sub.1d +L.sub.2 ·i.sub.2d

    φ.sub.2q =M·i.sub.1q +L.sub.2 ·i.sub.2q(2)

Basically, the vector control is designed to choose a suitable primarycurrent in order to establish the relations,

    φ.sub.2d M·i.sub.1d (=constant) and φ.sub.2d =0.

With this result, the slip frequency ω_(s) can be derived from thematrix (1) and be expressed by the equation: ##EQU3## If φ_(2d)=M·i_(1d) (=constant) and φ_(2q) =0 are not established, then the slipfrequency ω_(s) is expressed below: ##EQU4## In other words, the vectorcontrol is made to eliminate the second term of the above equation (4)by choosing the primary current supplied from the inverter 2 to themotor 1 and the primary frequency ω. The primary frequency ω isdetermined to be the slip frequency ω_(s) plus the speed command ω_(r)*, that, is, ω=ω_(s) +ω_(r) *, which is combined with equation (3) togive the following equation: ##EQU5## where Km represents a motorconstant specific to the induction motor. Since the motor constant Km isassumed to be fixed, the primary frequency ω can be influenced only bythe torque current i_(1q) and speed control command signal ω_(r) * sothat a speed control is made based upon the above vector control byregulating the primary current in a feedback manner.

Now, a discussion is made to the control system of FIG. 1. The vectorcontroller 10 comprises a vector processor 20 responsible for realizingthe above relations φ_(2d) =M·i_(1d) (=constant) and φ_(2q) =0, a speedcontroller 30, and a compensator 40 for correcting inputs of excitationcurrent command i_(1d) ^(*i), primary resistance set value r₁ ^(*i), andsecondary resistance set value r₂ ^(*i).

The vector processor 20 provides d-axis voltage component (excitationvoltage) V_(1d) and q-axis voltage component (torque voltage) V_(1q) byprocessing inputs of excitation current command i_(1d) *, torque currentsignal i_(1q) ' derived from the detected torque current i_(1q), andprimary frequency ω. This is made by executing the following matrixwhich is derived by putting φ_(2d) =M·i_(1d) (=constant) and φ_(2q) =0into equation (1): ##EQU6## That is, the excitation voltage V_(1d) isobtained by: multiplying the excitation current command signal i_(1d) *by primary resistance r₁ at a multiplier 21 to give a first product;

multiplying torque current signal i_(1q) ' by leakage coefficient σ,primary inductance L₁, and primary frequency ω at a multiplier 22 togive a second product; and

subtracting the second product from the first product at a subtracter23.

The torque voltage V_(1q) is obtained by:

multiplying primary inductance L₁ by excitation current command i_(1d) *to obtain a flux parameter φ(φ=L₁ ·i_(1d) *);

multiplying the detected torque current i_(1q) by primary resistance r₁at a multiplier 24 to give a third product;

multiplying primary frequency ω by flux parameter φ at a multiplier 25to give a fourth product; and

adding third and fourth products at an adder 26.

Thus obtained excitation voltage V_(1d) and torque voltage V_(1q) arefed to a coordinate transformer 3 where they are transformed, inaccordance with a phase angle demand θ, into the control voltage signalsVv, Vv, and Vw which regulates the inverter 2 for speed control of themotor 1. The phase angle demand θ is derived by integrating the primaryfrequency ω at an integrator 35, and is also utilized in a coordinatetransformer 5 for transformation of the sensed currents Iu, Iv, Iw fromthe current sensor 4 into the excitation current i_(1d) and torquecurrent i_(1q).

The speed controller 30 provides the torque current signal i_(1q) ' aswell as the primary frequency ω for determination of the excitationvoltage V_(1d) and torque voltage V_(1q) at the vector processor 20, inresponse to speed command signal ω_(r) * selected by the user and thesensed torque current i_(1q) from the current sensor 4. Included in thespeed controller 30 is a proportional plus integral (P-I) controller 31which provides the torque current signal i_(1q) ' as a delayed signal ofthe sensed torque current i_(1q), in order to eliminate over-responsivevector control which would otherwise appears during a transient periodof changing the motor speed. In the transient period, the operatingcondition of the motor can be expressed by the following matrix (7) ofequation, which is a modification of the above matrix (1) for stableoperating condition. ##EQU7## where I₁ and I₂ =primary and secondaryleakage inductance, respectively;

r₂ '=r₂ ·(M/L₂)² ; and

I₂ '=I₂ ·M/L₂.

The slip frequency ω_(s) in this transient period can be derived bycombining equation (6) into equation (7) and is expressed by thefollowing equation (8). ##EQU8## Consequently, the differential term ofequation (8) gives a corresponding effect to the slip frequency ω_(s)and therefore the resulting primary frequency ω(=ω_(s) +ω_(r) *) in thetransient period. When, for example, the speed command signal ω_(r) * isincremented at a time t₀. as shown in FIGS. 2A and 2B, torque currenti_(1q) responds to vary along a sharp curve indicated by dotted line inFIG. 2B. If the torque current i_(1q) is directly processed, theresulting slip frequency ω_(s) and the primary frequency ω suffer fromcorrespondingly marked variation, which causes the over-responsive speedcontrol. In view of the above, the P-I controller 31 gives the torquecurrent signal i_(1q) ', as indicated by solid line in FIG. 2B, which isa delayed signal of the sensed torque current i_(1q). The P-I controller31 operates to multiply a deviation between its output (delayed torquecurrent signal i_(1q) ') and input (sensed torque current i_(1q)) by asuitable constant and to integrate the deviation in such a manner as tozero the deviation calculated at a subtracter 32. The resulting delayedtorque current, i.e., torque current signal i_(1q) ' is multiplied bythe motor constant Km at a multiplier 33 to give slip frequency ω_(s)which is then added to speed command signal ω_(r) * at an adder 34 toprovide the primary frequency ω. As seen from FIGS. 2A and 2B, the useof delayed torque current of moderated waveform as the torque currentsignal i_(1q) ' results in a correspondingly moderated primary frequencyω, thereby avoiding over-responsive speed control and assuringconsistent vector control of the motor speed when changing the motorspeed.

Also in the present invention, the torque voltage V_(1q) is obtained bydirectly processing the sensed torque current i_(1q) rather than thedelayed torque current signal i_(1q) ' so as to improve speed responsecharacteristic under varying torque conditions, while the delayed torquecurrent signal i_(1q) * is utilized to determine the motor constant Kmfor maintaining the effect of avoiding over-responsive motor control.

In addition, the control system of the present embodiment includesschemes of providing correct motor constant Km for accurate vectorcontrol. As described hereinbefore, the motor constant Km is known to bespecific to the motor and can be input in the control system as a fixedvalue. However, if the motor constant Km should differ from an actualmotor constant, the vector controller fail to produce correct excitationand torque voltages V_(1d) and V_(1q), which in turn varies theexcitation current and the torque current in a direction of failing tosatisfy the relations φ_(2d) =M·i_(1d) (=constant) and φ_(2q) =0, whicheventually results in an erroneous vector control.

The erroneous variations in the excitation and torque voltages ΔV_(1d)and ΔV_(1q) (error voltages) due to an error in the motor constant Kmare expressed as follows:

    ΔV.sub.1d =Δr.sub.1 ·i.sub.1d *-σ·ΔL.sub.1 ·ω·i.sub.1q *

    ΔV.sub.1q =ΔL.sub.1 ·ω·I.sub.1d *-Δr.sub.1 ·i.sub.1q *                     (9)

where

Δr₁ =r₁ -r₁ *

ΔL₁ =L₁ -L₁ *

where

r₁ * and L₁ * are set values respectively for primary resistance andprimary inductance.

From equation (9), it is known that error voltages ΔV_(1d) and ΔV_(1q)in excitation and torque voltages are the consequence of errors Δr₁ andΔL₁ with respect to the set values r₁ * and L₁ *, that error voltagesresult critically from Δr₁ when primary frequency ω is small, and thaterror voltages result critically from ΔL₁ when primary frequency ω islarge. FIG. 3 illustrates corresponding variations in the excitationcurrent i_(1d) with respect to excitation current command i_(1d) * whenthe actual primary resistance r₁ differs from the primary resistance setvalue r₁ ^(*i). FIG. 4 illustrates corresponding variations in theexcitation current i_(1d) with respect to excitation current commandi_(1d) * when the actual primary inductance L₁ differs from the setprimary resistance L₁ ^(*i). Also known from equation (9) is that errorvoltages ΔV_(1d) and ΔV_(1q) is free from the error in ΔL₁ when primaryfrequency ω is zero, i.e., the motor is stalled.

Compensation for primary resistance r₁

In view of that the excitation voltage error ΔV_(1d) is not influencedby the primary inductance error ΔL₁ when the primary frequency ω iszero, a correct primary resistance r₁ * is obtained by regulating theexcitation current command i_(1d) * under a condition of stalling themotor. The compensation sequence starts by the speed controller 30issuing speed command ω_(r) * to stall the motor for a time period D₁,as shown in FIG. 5. During this period D₁, the speed controller 30actuates a switch regulator 41 for closing a switch 42 so as to connecta resistance identifier 43 in circuit between an output of a subtracter27 in the vector processor 20 and an adder 44. The identifier 43 is aP-I controller which gives an error voltage Δr₁ required for zeroing adifference Δi_(1d) between the excitation current command i_(1d) * andthe detected excitation current i_(1d). Thus obtained error resistanceΔr₁ is then added at the adder 44 to the initially set primaryresistance r₁ ^(*i) to give a true primary resistance r₁ * to beutilized in the vector processor 20.

Compensation for primary inductance L₁

After obtaining the true primary resistance, the motor controller 30gives speed command ω_(r) * to vary the speed for a time period D₂, asshown in FIG. 5, in order to obtain a true primary inductance L₁.Because of that the excitation current i_(1d) will fluctuate only by theeffect of primary inductance error ΔL₁ while the motor speed varies, andalso because of that the flux parameter φ(=L₁ ·i_(1d)) is constant forthe same rated induction motors, it is made to compensate for theexcitation current on behalf of compensating for the primary inductance.In this period D₂, the speed controller 30 actuates the switch regulator41 to open the switch 42 and close a switch 45 so as to connect anothercurrent identifier 46 in a circuit between the output of the subtracter27 and a subtracter 47. The current identifier 47 is a P-I controllerwhich gives an error current Δi_(1d) * required for zeroing a differenceΔi_(1d) between the excitation current command i_(1d) * and the sensedexcitation current i_(1d). Thus obtained error current Δi_(1d) * is thensubtracted at subtracter 47 from an initially set excitation currentcommand i_(1d) ^(*i) to provide the true current excitation commandi_(1d) * utilized in the vector processor 20.

Compensation for secondary resistance r₂

The system further necessitates to compensate for secondary resistancer₂ in order to give more consistent speed control based upon theprecisely determined motor constant Km, since the motor constant Km isalso a function of the secondary resistance, as seen from the equationbelow, and the secondary resistance r₂ will vary as a consequence ofcompensating the primary inductance L₁. ##EQU9## Since φ_(2d) is nearlyequal to M·i_(1d) and L₂ is nearly equal to L₁, the above equation issimplified into ##EQU10## Then, the above equation can be expressed by ain a simple format. ##EQU11## where φ is the flux parameter equal to L₁·i_(1d) (φ=L₁ ·i_(1d)).

A secondary resistance error Δr₂ * is correlated with the primaryinductance and is obtained at a resistance identifier 48 in accordancewith the following equation.

    Δr.sub.2 *=α·Δi.sub.1d *

where

α is a correlation factor and Δi_(1d) * is excitation current errorobtained in the above for correction of the primary inductance.

Thus obtained secondary resistance error Δr₂ * is added to an initiallyset secondary resistance r₂ ^(*i) to give true secondary resistance r₂*, which is subsequently multiplied by 1/φ at a multiplier 49 to givethe precise motor constant Km for determination of the slip frequencyω_(s) * and therefore the primary frequency ω.

Temperature compensation for primary resistance

The present system further contemplates to compensate for variation inthe primary resistance r₁ due to environmental temperature change. Anyprimary resistance error Δr₁ appearing after compensation of the primaryresistance r₁ and the primary inductance L₁ made in the time periods D₁and D₂ of FIG. 5, is thought to result solely from the temperature ofthe motor. In order to compensate for the primary resistance caused bythe temperature, the speed controller 30 operates to close the switch 42and open the switch 45 during a subsequent time period D₃, for obtainingthe primary resistance error Δr₁ * and providing the correct primaryresistance r₁ * in the same manner as described in the above, wherebyachieving consistent speed control free from temperature change.

The above periods D₁, D₂, and D₃ may be provided as default periods inconsideration of the rating and operating condition of the motor or maybe suitably altered during the operation of the motor.

Apart from the above compensations for determination of the correctmotor constant Km, the vector processor 20 includes a current regulator28 which operates in a proportional control mode to cancel thedifference Δi_(1d) which appears temporarily between excitation currentcommand i_(1d) * and the sensed excitation current i_(1d) due toinstantaneous fluctuation of the currents.

Second embodiment <FIG. 6>

FIG. 6 illustrates a vector control system in accordance with a secondembodiment of the present invention which is similar to the firstembodiment except that a voltage monitor 50 is included to monitor aprimary voltage V₁ from the output of coordinate transformer 3B, whichprimary voltage V₁ is expressed by the equation: ##EQU12## For easyreference purpose, like elements are designated by like numerals with asuffix letter of "B" and compensator 40 shown in the first embodiment isremoved from the figure. When the primary voltage V₁ is produced by thevector processor 20B becomes greater to such an extent as to givecontrol voltage exceeding a limit input voltage of the inverter, i.e.,the primary voltage V₁ saturates, the voltage monitor 50 responds tolower the flux parameter φ and therefore the resulting torque voltageV_(1q) until the primary voltage V₁ is lowered so as not to saturate andtherefore to lower the inverter input voltage below the limit voltage.Thus lowered flux parameter φ is also fed to multiplier 33B tocorrespondingly correct the motor constant Km in accordance with theabove equation (10), and therefore to correct the primary frequency ω,whereby assuring consistent speed control.

Third embodiment <FIG. 7>

FIG. 7 illustrates a vector control system in accordance with a thirdembodiment of the present invention which is similar to the secondembodiment except that an integrator 51 is added to give a delayed fluxparameter φ' for moderating the change of the motor constant Kmdetermined at multiplier 33C. For easy reference purpose, like elementsare designated by like numerals with a suffix letter of "C". When theprimary voltage V₁ is detected at the voltage monitor 50C to saturate,the voltage monitor 50C provides a lowering flux parameter φ tocorrespondingly lower the torque voltage V_(1q) in the manner asdiscussed in the second embodiment. Upon this occurrence, the integrator51 responds to integrate the lowering flux parameter φ to give delayedor moderate flux parameter φ' for determination of the motor constant Kmin accordance with the equation: ##EQU13## The resulting motor constantKm changes moderately so as to eliminate undesired fluctuation in themotor speed for improved speed control.

Fourth embodiment <FIGS. 8, 9A, and 9B>

FIG. 8 illustrates a vector control system in accordance with a fourthembodiment of the present invention which is identical to the firstembodiment but discloses a scheme of determining the secondaryresistance r₂. Like elements are designated by like numerals with asuffix letter of "D". In this embodiment, the secondary resistance r₂ isdetermined in accordance with the following equation: ##EQU14## Theabove equation (11) is obtained by rewriting the equation (8). Thus, thecorrect secondary resistance r₂ can be obtained by evaluating the slipfrequency ω_(s) and the torque current i_(1q). In order to cancel thesecond term of equation (11) for simplifying the calculation, it is madeto use a maximum torque current i_(1d)(max) which, as shown in FIG. 9B,has zero differential coefficient. That is, equation (11) is simplifiedinto ##EQU15## when taking into consideration that L₂ is nearly equal toM and φ is nearly equal to φ_(2d).

The slip frequency ω_(s) is evaluated by analyzing the waveform of thedetected torque current i_(1q) which is obtained by varying the motorspeed by one increment Δω over a time period T₂, as shown in FIGS. 9Aand 9B, under a condition of applying no load. Assuming that the motorspeed varies approximately linearly while incrementing the primaryfrequency by Δω, the slip frequency ω_(s) at the maximum torque currenti_(1q)(max) is obtained by the following equation: ##EQU16## where T₁ isa time required for torque current i_(1q) to reach its maximum from thestart of varying the primary frequency ω, and T₂ is a time required fortorque current i_(1q) to settles to zero.

Thus obtained slip frequency ω_(s) and the maximum torque currenti_(1q)(max) are substituted into equation (12) to give the correctsecondary resistance r₂, which is then utilized to determine the motorconstant Km in accordance with the above equation (10) for consistentvector control of the motor speed.

In order to determine the secondary resistance r₂, the system includes amotor constant operator 60 which receives the detected torque currenti_(1q) from the coordinate transformer 5D and outputs a speed signalω_(r) # to a selector 61. The selector 61 is normally set in position tofeed the speed command ω_(r) * to the adder 34D for determination of theprimary frequency ω by addition of the speed command ω_(r) * to the slipfrequency ω_(s) which is derived from the delayed torque current signali_(1q) ' obtained at the P-I controller 31D. The operator 60, whendetermining the secondary resistance r₂, issues a control signal S₁which causes the selector 61 to receive the speed signal ω_(r) # fromthe operator 60 instead of the speed command ω_(r) * and feed it to theadder 34D. At the same time, the controller 60 issues a control signalS₂ which opens a switch 62 inserted before the adder 34D so as toexclude the slip frequency cos resulting from the P-I controller 31D.Under this condition, the controller 60 outputs the speed signal ω_(r) #for rotating the motor at a fixed speed. After the motor reaches asteady-state condition, which is acknowledged by monitoring the torquecurrent i_(1q), the controller 60 increments the speed signal ω_(r) # byΔω and at the same time starts counting a time. After the motor reachesagain steady-state, the controller 60 stops counting the time to obtainthe above time period T₂, while obtaining above time period T₁ from themaximum torque current i_(1q) being monitored. Then, the operator 60executes the above equations (13) and (12) to determine the secondaryresistance r₂ and the motor constant Km. After determination of themotor constant Km, the operator 60 responds to make the selector 61 toreturn into its normal position and close the switch 62 so that thesystem is enabled to effect the vector control in the manner asdiscussed with reference to the first embodiment.

Fifth embodiment <FIGS. 10 to 12>

FIG. 10 illustrates a vector control system in accordance with a fifthembodiment of the present invention which is identical to the firstembodiment but discloses another scheme of determining the secondaryresistance r₂. Like elements are designated by like numerals with asuffix letter of "E". In this embodiment, the secondary resistance r₂ isdetermined by analyzing a waveform of a varying terminal voltage Vawhich appears in response to sudden interrupting the operating voltageto the induction motor 1E. When the operating voltage is suddenlyinterrupted, the terminal voltage Va will dampen over a relatively longperiod to zero in accordance with the following equation: ##EQU17##where M=mutual inductance;

ω_(r) =rotor speed of motor;

I₂₀ =effective value of secondary current appearing immediately afterinterruption of the operating voltage;

T₀ =damping factor (=L₂ /r₂).

Since this equation gives a relation that the terminal voltage isdependent upon the damping factor (T₀ =L₂ /r₂), the secondary resistancer₂ can be determined by analyzing the waveform of the terminal voltageVa provided that the secondary inductance L₂ is known. For this purpose,the system includes a voltage detector 70 connected to monitor theterminal voltage Va of the motor 1E, in addition to a motor constantoperator 60E which determines the secondary resistance r₂ and thereforethe motor constant Km based upon an output of voltage detector 70. Asshown in FIG. 11, the voltage detector 70 comprises a comparator 71which compares a voltage Va' indicative of the terminal voltage Va witha predetermined reference voltage Vref. The voltage Va' is limited belowa zener voltage by a combination of a resistor 72 and a zener diode 73.The reference voltage Vref is obtained by dividing the source voltage bya resistor 74. Firstly, the motor constant operator 60E issues a stopsignal to turn off all switching transistors of the inverter 2E tosuddenly interrupt feeding the operating voltage to the motor 1, inresponse to which the voltage Va' starts dampens, as indicated bywaveforms in FIG. 12, with the resulting decrease in amplitude. Whilethe voltage Va' exceeds the reference voltage Vref, the comparator 71outputs a signal to turn on a transistor 75 to flow a current through aphoto-diode 76, thereby turning on a photo-transistor 77 to produce anoutput pulse Vout. The output pulse Vout is then fed to a pulse-widthdetector 64 provided in the operator 60E, as shown in FIG. 13, so as togive a time period t₁ which extends from the sudden interruption of theoperating voltage and terminates at a time when the last output pulseVout disappears. Thus obtained time period t₁ is fed to a resistanceprocessor 65 to determine the secondary resistance r₂ in accordance withthe following equation: ##EQU18## where L₂ is a known secondaryinductance input to the processor 65, V₀ is an operating voltage appliedimmediately before the interruption thereof. The logarithmic valueK=ln(V₀ /Vref)is calculated at a logarithm processor 67 based upon V₀and Vref. Subsequently, the resulting secondary resistance r₂ is fed toa divider 66 where it is divided by the known flux parameter φ to givethe motor constant Km for determination of the slip frequency ω_(s)(=i_(1q) '·Km). With this scheme, the secondary resistance r₂ can bedetermined without relying upon additional voltage and speed detectors.

First modification of the fifth embodiment <FIG. 14>

FIG. 14 illustrates a modified scheme of determining the motor constantKm which is similar to the fifth embodiment except that the secondaryinductance L₂ is given by dividing the known flux parameter φ by thedetected excitation current i_(1d) at an additional inductance processor68. Since the flux parameter φ=i_(1d) ·M and is approximated into therelation φ=i_(1d) ·L₂ where M is nearly equal to L₂, the above equation(14) is modified into the following equation (15): ##EQU19## Thesecondary resistance r₂ is obtained in accordance with equation (16) andis then processed in the same manner as in the fifth embodiment. In FIG.14, like elements are designated by like numerals with a suffix letterof "F" for easy reference purpose.

Second modification of the fifth embodiment <FIG. 15>

FIG. 15 illustrates a second modified scheme of determining the motorconstant Km which is similar to the fifth embodiment except that thesecondary resistance r₂ is determined in accordance with the followingequation (16): ##EQU20## where t₂ =cycle of the output pulse Voutfirstly appearing immediately after the interruption of the operatingvoltage as defined in FIG. 12; and

t₃ =cycle of the last appearing output pulse Vout as defined in FIG. 12.In this modification, like elements are designated by like numerals witha suffix letter of "G". In response to the output pulse Vout fromvoltage detector 70G, the pulse-width detector 64G provides thus definedparameters t₁, t₂, and t₃ to resistance processor 65G as well as tologarithm processor 67G which in turn provides a logarithm value K=ln(V₀·t₂ /Vref·t₃) to resistance processor 65G. Then, resistance processor65G calculates r₂ in accordance with equation (16) based upon the inputsof thus obtained t₁, K, and the known L₂. The resulting secondaryresistance r₂ is divided by the known flux parameter φ at divider 66Gfor determination of the motor constant Km.

Third modification of the fifth embodiment <FIG. 16>

FIG. 16 illustrates a modified scheme of determining the motor constantKm which is similar to the modification of FIG. 15 except that thesecondary inductance L₂ is given by dividing the known flux parameter φby the detected excitation current i_(1d) at additional inductanceprocessor 68H. Since the flux parameter φ=i_(1d) ·M and is approximatedinto the relation φ=i_(1d) ·L₂ where M is nearly equal to L₂, the aboveequation (16) is modified into the following equation (17): ##EQU21##The secondary resistance r₂ is obtained at resistance processor 65H inaccordance with equation (17) and is then processed at divider 66H inthe same manner as in the modification of FIG. 15 to determine the motorconstant Km. In FIG. 16, like elements are designated by like numeralswith a suffix letter of "H" for easy reference purpose.

What is claimed is:
 1. A vector control method for controlling a rotorspeed of an induction motor by use of an inverter which provides an ACcurrent of varying frequency to said induction motor, and a vectorcontroller which provides control voltage Vu, Vv, Vw, in response to anexcitation current command i_(1d*) indicative of an excitation currentbeing fed to said induction motor, a desired rotation speed commandω_(r*), and a primary frequency ω, for controlling said inverter to varysaid rotor speed, said method comprising the steps of:detecting aprimary current being fed to said induction motor; analyzing saiddetected primary current to derive therefrom an excitation currenti_(1d) and a detected torque current i_(1q) ; multiplying a torque valuerepresented by said detected torque current i_(1q) by a predeterminedmotor constant K_(m) to obtain a slip frequency ω_(s) ; and adding thusobtained slip frequency ω_(s) to said rotation speed command ω_(r*) todetermine said primary frequency ω (ω=ω_(r*) +ω_(s)); calculating adeviation between said delay torque current i_(1q') and said detectedtorque current i_(1q) and supplying said deviation to a proportionalplus integral controller, said proportional plus integral controllerproducing as an output an updated delayed torque current i_(1q') as saidtorque value for determining said primary frequency ω.
 2. The method asset forth in claim 1, further including the step of correcting saidexcitation current command i_(1d) * in a direction of zeroing thedifference between said excitation current command i_(1q) * and saiddetected excitation current i_(1d).
 3. The method as set forth in claim1, wherein said vector controller additionally receives a primaryresistance set value r₁ * indicative of a primary resistance r₁ of saidinduction motor in determining said control voltage, said method furtherincluding the steps of:supplying primary current and holding said motorto stall, and correcting said primary resistance set value r₁ * in adirection of zeroing a difference between said excitation currentcommand i_(1d) * and said detected excitation current i_(1d), under acondition of supplying said primary current to said induction motorwhile holding said motor to stall, and subsequently correcting saidexcitation current i_(1d) * in a direction of zeroing the differencebetween said excitation current i_(1d) * and said detected excitationcurrent i_(1d), under a condition of varying the rotation speed.
 4. Themethod as set forth in claim 3, wherein said method further includes thestep of:correcting again said corrected primary resistance set valuer₁ * in a direction of zeroing a difference between said excitationcurrent command i_(1d) * and said detected excitation current i_(1d),after correcting said excitation current command i_(1d) *.
 5. The methodas set forth in any one of claims 2 to 4, wherein said vector controlleradditionally receives a secondary resistance set value r₂ * indicativeof a secondary resistance and a primary inductance L₁ of said inductionmotor in determining said control voltage, said method further includingthe step of:correcting said secondary resistance set value r₂ * in adirection of zeroing a difference between said excitation currentcommand i_(1d) * and said detected excitation current i_(1d) ; anddetermining said motor constant Km in accordance with a followingequation: ##EQU22## where r₂ is secondary rotor resistance, φ is a fluxparameter equal to L₁ ·i_(1d) * (φ=L₁ ·i_(1d) *).
 6. The method as setforth in claim 1, wherein said vector controller acknowledges a primaryresistance r₁, a primary inductance L₁, and a predetermined equivalentleakage inductance of said induction motor for determination of saidcontrol voltage, said method further including the steps of:multiplyingsaid primary inductance L₁ by said excitation current command i_(1d) *to obtain a flux parameter φ; obtaining a first product of said primaryresistance r₁ and said excitation current command i_(1d) *; obtaining asecond product of said delayed torque current i_(1q) ', said equivalentleakage inductance σ·L₁, and said primary frequency ω; subtracting saidsecond product from said first product to provide an excitation voltageV_(1d) ; obtaining a third product of said detected torque currenti_(1q) and said primary resistance r₁ ; obtaining a fourth product ofsaid flux parameter φ and said primary frequency ω; adding said thirdproduct and fourth product to provide a torque voltage V_(1q) ; andprocessing said excitation voltage V_(1d) and torque voltage V_(1q) togive said control voltage.
 7. The method as set forth in claim 6,further including the steps of:monitoring a primary voltage V₁ ; andvarying said flux parameter φ in accordance with said monitored primaryvoltage V₁ in order to correct the primary frequency ω which is afunction of said flux parameter φ.
 8. The method as set forth in claim7, further comprising the step of setting said motor constant Km equalto r₂ /φ, in which r₂ represents a secondary resistance of saidinduction motor.
 9. The method as set forth in claim 8, furthercomprising the step of varying said motor constant Km by integratingsaid varying flux parameter φ.
 10. The method as set forth in claim 1,wherein said motor constant Km varies in proportion to a secondaryresistance r₂ of said induction motor, said method further including thefollowing steps of:a) providing a time frame where no said slipfrequency ω_(s) is obtained from said delayed torque current i_(1q) ';b) incrementing said rotation speed command ω_(r) * by Δω within saidtime frame and under no load condition; c) analyzing thus obtainedwaveform of said detected torque current i_(1q) to determine saidsecondary resistance r₂ and therefore determine said motor constant Km.11. The method as set forth in claim 10, wherein said step c) comprisesthe sub-steps of:determining a maximum torque current i_(1q)(max) fromsaid waveform; obtaining a first time period T₁ when said detectedtorque current i_(1q) increases from a start value just beforeincrementing said rotation speed command value ω_(r) * to said maximumtorque current i_(1q)(max) ; obtaining a second time period T₂ when saiddetected torque current i_(1q) increases from said start value andsettles to a first value past said maximum torque current i_(1q)(max) ;and determining said secondary resistance r₂ in accordance with afollowing equation: ##EQU23## wherein φ is a predetermined fluxparameter.
 12. The method as set forth in claim 1, wherein said motorconstant Km varies in proportion to a secondary resistance r₂ of saidinduction motor, said method further including the following steps of:a)suddenly supplying an operating voltage to said induction motor tomeasure a time period t₁ when a terminal voltage Va' of said inductionmotor dampens to a reference voltage Vref; b) determining said secondaryresistance r₂ in accordance with a following equation: ##EQU24## whereinV₀ is a voltage which has applied to said induction motor immediatelybefore interrupting said operating voltage, and L₂ is a secondaryinductance of said induction motor.
 13. The method as set forth in claim1, wherein said motor constant Km varies in proportion to a secondaryresistance r₂ of said induction motor, said method further including thefollowing steps of:a) suddenly supplying an operating voltage to saidinduction motor to measure a time period t₁ when a terminal voltage Va'of said induction motor dampens to a reference voltage Vref; b)determining said secondary resistance r₂ in accordance with a followingequation: ##EQU25## wherein φ is a predetermined flux parameter, i_(1d)is said detected excitation current, and V₀ is a voltage which wasapplied to said induction motor immediately before interrupting tosupply said operating voltage.
 14. The method as set forth in claim 1,wherein said motor constant Km varies in proportion to a secondaryresistance r₂ of said induction motor, said method further including thefollowing steps of:a) suddenly supplying an operating voltage to saidinduction motor to measure a time period t₁ when a terminal voltage Va'of said induction motor dampens to a reference voltage Vref; b)obtaining a first cycle t₂ for said terminal voltage Va' appearingimmediately after interrupting to supply said operating voltage; c)obtaining a last cycle t₃ for said terminal voltage Va' appearingimmediately before damping to said reference voltage Vref; and d)determining said secondary resistance r₂ in accordance with a followingequation: ##EQU26## wherein L₂ is a secondary inductance of saidinduction motor, and V₀ is a voltage which was applied to said inductionmotor immediately before interrupting said operating voltage.
 15. Themethod as set forth in claim 1, wherein said motor constant Km varies inproportion to a secondary resistance r₂ of said induction motor, saidmethod further including the following steps of:a) abruptly interruptingto supply an operating voltage to said induction motor to measure a timeperiod t₁ during which a terminal voltage Va' of said induction motordampens to a reference voltage Vref; b) obtaining a first cycle t₂ forsaid terminal voltage Va' appearing immediately after interrupting tosupply said operating voltage; c) obtaining a last cycle t₃ for saidterminal voltage Va' appearing immediately before damping to saidreference voltage Vref; and d) determining said secondary resistance r₂in accordance with a following equation: ##EQU27## wherein φ is apredetermined flux parameter, i_(1d) is said excitation currentcomponent, and V₀ is a voltage being applied to said induction motorimmediately before interrupting said operating voltage.